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A355808
a(n) is the number at the apex of a triangle whose base contains the distinct powers of 2 summing to n (in ascending order), and each number in a higher row is the difference of the two numbers directly below it; a(0) = 0.
2
0, 1, 2, 1, 4, 3, 2, 1, 8, 7, 6, 5, 4, 1, 2, 1, 16, 15, 14, 13, 12, 9, 10, 9, 8, 1, 2, -3, 4, 3, 2, 1, 32, 31, 30, 29, 28, 25, 26, 25, 24, 17, 18, 13, 20, 19, 18, 17, 16, 1, 2, -11, 4, -5, -6, -15, 8, 7, 6, 9, 4, 1, 2, 1, 64, 63, 62, 61, 60, 57, 58, 57, 56, 49
OFFSET
0,3
FORMULA
a(n) <= n with equality iff n = 0 or n is a power of 2.
a(2*n) = 2*a(n).
EXAMPLE
For n = 27:
- we have the following triangle:
-3
5 2
1 6 8
1 2 8 16
- so a(27) = -3.
PROG
(PARI) a(n) = { my (b=vector(hammingweight(n))); for (k=1, #b, n-=b[k]=2^valuation(n, 2)); while (#b>1, b=vector(#b-1, k, b[k+1]-b[k])); if (#b, b[1], 0) }
CROSSREFS
See A355807 for similar sequences.
Cf. A348296.
Sequence in context: A302436 A283167 A355807 * A080079 A341707 A347820
KEYWORD
sign,base
AUTHOR
Rémy Sigrist, Jul 18 2022
STATUS
approved